Cutter for and method of cutting gears



June 2, 1942.

E. WILDHABER CUTTER FOR AND METHOD OF CUTTING GEARS Filed April 17, 19379 Sheets-Sheet l Ernes? M/ZLZCZ/maber mum;

Jum: 2, 1942- E. WILDHABER 2,285,133

7 CUTTER FOR AND METHOD OF CUTTING GEARS Filed April 17, 193'? 9Sheets-Sheet 2 Ernest Zdhazbe 3nve'ntor Qttomeg June 2, 1942. E.WILDHABER 2,285,133

CUTTER FOR AND METHOD OF CUTTING GEARS Filed April 17, 1937 9Sheets-Sheet 3 Erneszl Zhwentor (Ittorneg June 2, 1942. E. WILDHABER2,235,133

CUTTER FOR AND METHOD OF CUTTING GEARS Filed April 17, 1957 9Sheets-Sheet 4 160 iiez 161 165 .EkI'MEESZ WiZdhGbe -3fventor June 2,1942." E. WILDHABER 2,285,133

CUTTER FOR AND METHOD OF CUTTING GEARS Filed April 17, 1937 9ySheets-Sheet 5 June 2, 1942. E. WILDHABER CUTTER FOR AND METHOD OfCUTTING GEARS Filed April 17, 1937 9 Sheets-Sheet 6 Zhwehtor 'Ernesi'VVilcZ/ Lczbr attorney,

June 2, 1942. E. WILDHABER CUTTER FOR AND METHOD OF'CUTTING GEARS FiledApril 17, 1957 9 Sheets-Sheet 7 June 2;, 1942.

E. WILDHABER CUTTER FOR AND METHOD OF 'CUTTING GEARS Filed April 17,1937 9 Sheets-Sheet 8 3nventor v ErnesZ mldhg er 4| |||||||||1lllllllllll June 2, 1942. E. WILDHABER 2,235,133

. CUTTER FOR AND METHOD OF CUTTING GEARS Filed April 17, 1937 9sheets-sheet 9 @Q Ft; 59

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EFT? 65' Z l'inventor Gttorneg Patented June 2, 1942 orrice CUTTER FORAND METHOD OF CUTTING GEARS Ernest Wildhaber, Irontlequoit, N. Y.,assignor to Gleason Works, Rochester, N. Y., a corporation of New YorkApplication April 17, 1937, Serial No. 137,531

42 Claims. (Cl. 90-=-5) roll'anol' in a single pass of a tool and insuch way 7 that the teeth of the gear will taper properly in depth andwidth from end to end.

To these ends, it is a further object of the invention to provide amethod of generating a tapered gear or pinion in which the toolrepresents two or more tooth sides of a basic gear or crown gear and hasa plurality of cutting edges lying in imaginary surfaces representingsuch tooth sides, and in which the cutting motion of the tool is timedwith the generating roll in such manner that the cutting edges of thetool are coordinated with and adapted to cut at definite points alongthe generated tooth surfaces and in which the cutting profile or contourformed by a top and opposite side cutting edges of the tool may varyalong saidimaginary surfaces and be adapted to the portion of the geartooth to which it is coordinated;

Another object of the invention is to provide a gear-cutting tool thathas a'plurality of cutting edges so arranged that successive cuttingedges form a cutting portion of varying profile or contour which differsfrom the profile or contour of the tooth spaces of the gear to be out.

A further object of the invention is to provide a gear cutting tool ofthe above character whose profile or contour has straight sides butchanges in size along the imaginary cutting surface or thread.

Still another object of the invention is to provide a gear generatingtool having a plurality of cutting edges arranged in an imaginarysurfacewhose cutting profile differs from the profile of the gear teeth tobecut and changes along said imaginary surface'and in which the number ofcutting edges is large'enough completely to Another object of theinvention is to provide a method and tool for generating tapered gearsin which the tool has cutting edges arranged in" a surface of revolutionor in a helicoidal surface about an axis and in which the tool isrotated on' said" axis so that the tool makes only one revolution duringgeneration of a tooth surface or a plurality of tooth surfaces of thegear, and in which the blank is indexed once for each revolution of thetool. I

A further object of the invention is to provide a tool of thesingle-cycle type for cutting tapered gears having a plurality ofcutting edges arranged circularly part-way around its periphery with agap between the last and first blades and in which the number of cuttingedges is large enough to completely form a tooth surface of a gear blankwith desired taper in depth by enveloping, or generating cuts in onerevolution of thetool. I

A further object of the invention is to provide a tool of the characterdescribed by the use of which two sides of a tooth space of alongitudinally curved tooth tapered gear maybe cut simultaneouslywithout bias bearing and without the necessity for any correcting motionbetween cutter and blank.

Still another object of the invention is to provide an improved methodand improved cutting apparatus for rough-cutting spiral bevel and hypoidpinions to provide roughed-out tooth slots which will taper in width anddepth from I end .to end.

form a tooth surface through generation or en-. 7

velopment.

Still another object of the invention is to pro- 5 contact the generatedtooth surface formed by x the finish cutting edges.

A still further object of the invention is to provide an improved methodand tool for shaving tapered gears. 1

Still further objects of the invention will appear hereinafter from thespecification and from the recital of the appended claims.

. Fig. 1 is a diagrammatic view, showing a crown gear fragmentarily andillustrating diagrammatically the conditions to be fulfilled in order tocut simultaneously two sides of 'a tooth space of a longitudinallycurved tooth gear or pinion with the correct tooth taper;

.Fig. 2 is a fragmentary sectional view showing the generating rollduring generation of a tooth space of such a gear by the method of thepresent invention;

Fig. 5 is a fragmentary sectional view, illustrating more or lessdiagrammatically the construction of a face-mill gear cutter builtaccording to one modification of this invention and showing in sectionthe blade of the cutter which is adapted to cut at the large end of thetooth space of a tapered gear;

Figs. 6 and 7 are views of the blades of this cutter which are adaptedto cut at the middle of the tooth space and at the small end of thetooth space, respectively;

' Figs. 8 and 9 are a fragmentary perspective view of a longitudinallycurved tooth gear and a section taken lengthwise of the tooth space ofthis gear, respectively, illustrating why the blade of the cutter, whichcuts at the small end of the tooth, will clear the large end of thetooth space and not afiect the finished shape of the tooth space at itslarge end;

Figs. 10 and 11 are views corresponding to Figs. 8 and 9, respectively,and showing the p0- sition of the gear at a further point in thegenerating roll and illustrating why the blade of the cutter which cutsat the large end of the tooth space will clear the small end of thetooth space and not affect the finished shape of the small end of thetooth space;

Figs. 12: and 13 are a plan and a developed View, respectively, of oneform of face-mill gear cutter made according to the present invention;

Fig. 14 is a section on the line |4-I4 of Fig. 13;

Fig. 15 is a developed view of a cutter which is adapted to rotate inthe opposite direction from that of the cutter shown in Figs. 12 and 13;

Fig. 16 is a fragmentary diagrammatic view illustrating the constructionof a cutter made according to a still further modification of thepresent inventionand adapted to cut during both the forward and returngenerating rolls;

Fig. 17 is a diagrammatic illustration of a cutter made according to astill further embodiment of this invention;

Fig. 18 is a diagrammatic view illustrating the relation between acutter such as shown in Fig. 1'7 and the gear being cut and showing howsuch a cutter may be employed to cut gears without bias bearingaccording to one embodiment of this invention;

Fig. 19 is a view similar to Fig. 18, but showing the relationshipswhich exist when the cutter is rotated in the opposite direction;

Fig. 20 is a fragmentary axial section of the cutter taken in a planenormal to a side of the gear tooth space being operated upon, andillustrating further principles of the invention;

Fig. 21 is a diagrammatic developed view of a cutter such as might beemployed in the arrangement illustrated in Fig. 18;

Fig. 22 is a diagrammatic View showing in elevation four spaced bladesof the cutter shown in Fig. 21, and illustrating the relation of theseblades to one another, the blades shown being located in the cutter atthe positions denoted by the lines AA, BB, CC and DD, respectively inFig. 21;

Fig. 23 is a developed view of a cutter such as might be employed forcutting a gear according to the method illustrated in Fig. 19;

Fig. 24 is a View showing three blades of this cutter in elevation andillustrating the relationship of these blades to one another, the bladesshown being those located at the positions denoted by the lines EE, FFand GG, respectively, in Fig. 23;

Fig. 25 is a developed view of a cutter for cutting gears according tothe method illustrated diagrammatically in Fig. 19 but which will rotatein use in a direction opposite to the direction of rotation indicated inFig. 19 and which, therefore, will cut in the opposite direction of thegenerating roll;

Fig. 26 is a diagrammatic view showing in elevation, three of the bladesof this cutter and illustrating the relationship between these blades,

the blades shown being located at the positions denoted by the linesHI-I, II and JJ in Fig. 25;

Figs. 27 and28 are fragmentary sectional and plan views, respectively,illustrating one form of female cutter for cutting spiral bevel andhypoid pinions according to this invention and showing one method ofemploying the same;

Figs. 29 and 30 are corresponding views illustrating another method ofcutting pinions with a female'tool according to the present invention;

Fig. 31 is a diagrammatic View showing the shape of different blades ofa female cutter made according to one embodiment of this invention;

Fig. 32 is a corresponding view showing several blades of a cutter madeaccording to a different embodiment of the invention;

Figs. 33 and 34 are a developed side elevation and a plan view,respectively, of a female cut ting tool made according to thisinvention;

Fig. 35 is a developed side elevation and Fig. 36 a developed sectionalView of a shaving tool corresponding to the cutting tool shown in Figs.33 and 34 and constructed according to one embodiment of this invention;

Figs. 37, 38 and 39 are sections through this tool taken on the linesKK, LL, MM, respectively, of Figs. 35 and 36;

Figs. 40 to 42 inclusive'are views illustrating further possiblemodifications of the invention and showing various profile shapes whichmay be used upon blades of cutters constructed according to theinvention.

In the present invention a tool is used which has a plurality of cuttingedges, each of which is constructed to operate at a definite point alongthe length of a tooth surface of a gear. The cutter is intended to cutthe whole length of the tooth surface in a single pass through a toothspace. For a tapered gear, then, there will be one blade of the cutterwhich will cut at the large end of the gear tooth and another bladewhich will cut at the small end of the tooth and between these blades,there will be blades to cut at all intermediate points along the lengthof the tooth. The method is adapted for the production only of gearswhich have 1ongitudinally inclinedteeth and in a generating orenveloping operation. The blade which is adapted to cut at the large endof the tooth clears the small end of the tooth and vice-versa because ofthe longitudinal inclination of the teeth being cut and of thegenerating roll or enveloping action of the cutter in the cutting of thetooth surfaces'of the blank. For finishcutting, a sufficiently largenumber of blades are provided in the cutter to generate tooth surfacesof the required smoothness of finish.

For cutting spiral bevel and hypoid gears, a cutter of the single cycletype is preferably employed. Such a cutter has a plurality of cuttingblades'a'rranged circularly part-way around its periphery with a gapbetween the last and first blades. When constructed according to thepresent invention, the blades of the cutter vary in shape around theperiphery of the'cutter, each blade being adapted, as above indicated,to cut at some particular point along the length of a tooth of the gear.In the cutting operation, the cutter is rotated in engagement with theblank while a relative rolling movement is produced between the cutterand blank. In one embodiment of the invention, the cutter cuts onlyduring roll in one direction and the blank is indexed and the returnroll takes place while the gap in the cutter is abreast of the blank. Inanother embodiment of the invention, the cutter is designed so that itwill cut during both the forward and return rolls and the blank isindexed when the tooth surface or tooth surfaces have been cut and thegap in the cutter is abreast of the blank. 1

Cutters made according to the invention ordinarily follow usual practicein that the cutting blades have all the same pressure angle. Thevariation in point-width required between the blades that are adapted tocut at different points along the length of. a tooth may be obtained,however, in various ways. In one embodiment of the invention, the bladesare so made that opposite sides of the blades converge in points whichlie on a circle lying in a plane perpendicular to the axis of the cutterand the variation in height 'of the different blades produces thevariation in point-width.

In longitudinally curved tooth tapered gears having teeth which-taper inheight from end to end, however, a bias bearing condition is ordinarilyencountered, namely, a bearing or tooth surface contact which extendsdiagonally of the tooth surface from end to end thereof. This bearingcondition is objectionable and various meanshave been employed. toeliminate it and to produce a bearing which will extend parallel orapproximately parallel to the pitch line of a pair of mating gears. Onemethod that has been proposedfor elimination of bi-as bearing is toimpart to the cutter a helical motion during generation, that is, tofeed the cutter axially relative to the gear blank as the cutter rotateson its axis during the generating roll. Such an axial motion makes foradditional complication, however, in the design and construction of thegearcutting machine.

It is possible to eliminate this bias bearing condition very simply withthe present invention along the length of a'tooth, but in addition havethe described helical arrangement of thepoints of intersection of theirside cutting edges so that as the cutter is rotated in engagement withthe gear blank during the generating roll, successive blades have ineffect a displacement relative to the gear blank as though the cuttermade according to the first described embodiment of this invention werebeing displaced axially during its rotation. In other words, the helicalmotion heretofore proposed for elimination as bias bearing is actuallybuilt into the cutter.

' To obtain proper conjugacy between two members of a pair of taperedgears whose tooth surfaces are out two sides simultaneously, it isproposed in one modification of the present invention to out one memberof the pair with a female tool which is complementary to the male toolused in the cutting of the other member of the pair. As with the priordescribed embodiments ofthe invention, it is preferred to make thisfemale tool of the single cycle type. The female cutter may be employedeither in a generating operation where the tool represents a tooth spaceof a crown gear or other basic gear to which the blank is to begenerated conjugate or in a generating'operation in which the toolrepresents a tooth space of the gear with which the gear being cut is tomate. The blades of the female cutters like the blades of tools madeaccording to previously mentioned embodiments of the present inventionvary in shape around the cutter. The blades may be made all of the samepoint-width or of varying point-width.

It will be obvious that the invention is not limited to the cutting ofgears, but may also be employed in the shaving, lapping or burnishing ofgears. Thus, instead of a tool having a plurality of relieved cuttingedges such as is employed in a cutting operation, a tool having aplurality of unrelieved cutting edges may be substituted and used toshave a gear whose tooth surfaces have previously been cut toapproximately finished size and shape. A shaving tool made according tothe present invention, like the cuttingtools already described, hasdifferent cutting edges which are adapted to shave at different .pointsalong the length of a tooth surface of the gear being shaved. Theshaving tool, like the cutting tool, is also preferably provided withcutting edges only part-way around its periphery and there is a gapbetween the last and first edge to permit of indexing the gear when thegap in the tool is abreast of the gear.

Shaving tools constructed according to' the present invention areadapted to operate in a generating or enveloping process and a toothsurface or a pair of tooth surfaces of a gear-will be completely shavedafter a complete pass of the shaving toolthrough a tooth space of thegear.

The invention is not restricted to the finishcutting of gears, but maybe employed with advantage for rough-cutting gears also where the blankand cutter are rolled relative to, one another during the roughingoperation. Through use of cutters constructed according to the-presentinvention, a'gear can be roughed out with tooth slots tapering in depthand width from end to end and hence a gear can be roughed closer tofinished tooth depth. The application of the present invention to therough-cutting of gears is described specifically in a separateapplication,

Serial No. 279,523, filed June 16, 1939, which is a continuation in partof the present application. The present application is intended to coverthe invention broadly and more specifically, the finishing of gearseither from the solid or from a previously roughed gear blank. Thecutters employed for the present invention may have either straight sidecutting edges or cutting edges of curved profile and if a profilecurvature is used, this may be of any suitable character. I

Reference will now'be had'to the drawings for a more detaileddescription of the invention.

The invention is particularly useful for simultaneously forming two ormore tooth sides of a gear or pinion. We shall first derive, therefore,

the relationships or conditions to be fulfilled for simultaneouslycutting two sides of a pinion or gear with correct tooth taper.

In Fig. 1, a crown gear 59 is shownand in Fig. 2 there is illustrated aface-mill gear cutter 5| in engagement with a gear blank 52 which is tobe generated conjugate to such a crown gear.

The cutter in its operation is to'represent two tooth sides of the crowngear and is intended to generate simultaneously two tooth surfaces onthe gear 52'which will be conjugate to the tooth surfaces of the crowngear 50.

In order that a cutter 5| may represent simultaneously two tooth sidesof the crown gear of natural tooth taper, the two tooth sides 53 and 54of the crown gear should have the same spiral angle at the pitch surfaceof the crown gear, that is, the tooth sides should be equally inclinedto radii 55 and 56, respectively, drawn from the apex 5'! of the crowngear to mean points 59 and 69, respectively, at equal distances from theapex 51. In other words, the two pitch-line elements of the toothsurfaces 53 and 54 should be obtainable by simply rotating a mean pitchline element 6| first in one direction and then in the other about thecrown gear axis 62.

If the gear which is to mate with the gear 52 is also generatedconjugate to a crown gear which fulfills the above requirements andwhich is complementary to the crown gear 50, the gear 52 and its matewill mesh correctly with one another.

Like the pitch-line elements of the tooth surfaces 53 and 54, thenormals 63 and 64, respectively, to the pitch-line elements may beobtained by turning the normal 65 at mean point 66 of pitch-line element6| about the crown gear axis 62. It is therefore evident that all threenormals 63, 64 and 65 have the same distance from the crown gear axis 62and from crown gear apex 5'! and are tangent to a circle 68 concentricwith the crown gear apex.

The normals 63 and 65 intersect at a point 69 which lies on a line Tildrawn from the crown gear apex 51 perpendicular to the projected meannormal 55.

Let A be the mean cone distance, that is, the distance 5l-56; let 1' bethe mean cutter radius, which is substantially equal to the distance66-42, 12 being the point of intersection of the cutter axis 13 with thepitch plane 14 (Fig. 2) of the crown gear, which plane is, of course,perpendicular to the crown gear axis 62.' Let 1/1 denote the spiralangle of the tooth surfaces of the crown gear at the mean point 66 andlet 4; denote the pressure angle of the tooth surfaces of the crowngear, that is, the inclination of the actual tooth normals 63 and 64 inspace with respect to the pitch plane 14 of the crown gear.

In order that the face-mill cutter 5| may embody two tooth surfaces 53and 54 of the crown gear simultaneously, it is necessary that the cut.ter axis 13 should be so inclined to the pitch plane 14 of the crowngear that it passes through tooth normal 64 as well as tooth normal 63.The cutter axis 13 intersects tooth normal 54 in a point 16 and itintersectstooth normal 63 in a point 11.

We shall now determine the inclination i of the cutter axis 13 withrespect to' the crown gear axis 62.

The vertical distance, in the direction of the crown gear axis 62 of thepoints 16 and 77 from one another is 2? tan 4). The horizontal distance,that is, the projected distance 1-5-1! in Fig. 1 very closelyapproximates a distance 69-72 cos t -arc angle (766977) A 1r 0 mm m Inthe Gleason system of spiral bevel gears, the

dedendum of a miter gear or the average dedendum tan 11 1.038 be: P andthe dedendum angle dais obtained from the formula Formula (1) isapplicable broadly to face-mill gear cutters of the conventional type aswell as to face-mill gear cutters of the single cycle type. Theface-mill cutter should be positioned relative to the gear 52 to be cut,whose axis is at 8 2, so that the line I5 containing the points ofconvergence on its side cutting edges will be inclined to the pitchplane 14 of the crown gear at the angle 2 (Fig. 2). When theconventional face-mill 5! is positioned, however, so that it includesthe said angle 1' with relation to the pitch plane 14 of the crown gear,it will not cut the desired dedendum angle on the gear 52, but is boundto cut a tooth bottom along dotted line 80 which is inclined at angle 2'to the pitch plane M. This arrangement, however, results in an excessivetooth height at the large end of the tooth and in a subnormal toothheight at the toe or small end of the tooth.

This undesirable condition is overcome with the present invention forthe desired standard tooth proportions and the desired root line 82,which is inclined to the pitch plane 14 at the standard dedendum angleda, may be obtained with a single cycle cutter constructed according tothe present invention each of whose finish-cutting edges is arranged tocut only one portion of the tooth space of the gear blank.

One cutting edge cuts the root portion of the tooth space at the toe orsmall end only. An other cutting edge, possibly a quarter of a turn fromthe first named cutting edge, cuts the root portion at the center only.Still another blade cuts the root portion of the gear blank at the largeend of the tooth only. For this reason, the blades or cutting teeth ofthe cutter may be made of varying heightso that the desired root line 82may be cut all along the length of the tooth. One cutting blade in thecutter is made just high enough to cut the desired depth at the toe orsmall end of the tooth. The height of the middle cutting blade is madeto fit the height of the tooth surface at the middle portion of thelength of the tooth, and the cutting blade which is adapted to form theroot portion at the heel or large end of the tooth is made just highenough to cut the desired depth at that point.

Ihe heights of intermediate blades change gradually, of course.

The opposite side-cutting edgesof the cutter are preferably madestraight and preferably will be madewith positive pressure angles sothat when prolonged, the opposite side-cutting edges intersect in apoint and form an inverted V. This V-shape 83 is constant for all thefinishing blades, that is, for all blades of the cutter which havecontact with and cut the finished tooth surfaces. In this respect, theblades of a cutter made according to the present invention are the sameas for a conventional face-mill gear cutter. However, in the new cutter,different blades are made of varying heights so that they occupy largeror smaller portions of the inverted V and so that the side cutting edgesas well as the tip cutting edges of the blades vary in length fordifferent blades disposed at different points around the cutter. Inother words, the total cutting contour or profile formed by the tip andopposite side cutting edges or different blades of the cutter variesaround the finishing portion of the cutter.

In the cutting of a gear 52, then, according to the present invention,the cutter is preferably of the single cycle type, that is, it hasblades arranged only part-way around its periphery and there is a gapbetween the last and first blades to permit indexing the blank when thisgap is abreast of the blank without relative withdrawal of the cutterfrom the work. The blades vary in height as described, and this cutteris rotated on its axis 13 in engagement with the gear blank while arelative rolling movement is produced between the cutter and blank asthough the gear to be cut were rolling in mesh with the crown gearrepresented by the tool.

It is not necessary that the gear be generated conjugate to a true crowngear, but it may also be generated conjugate to a nominal crown gear, asis the case when cutting gears according to the usual practice. As arule, the latter method of generation is preferable inasmuch as someprofile mismatch may be obtained on the gear tooth in this way. In orderto generate the gear, in this Way, the cutter axis may be positioned sothat it is parallel to the axisof the cradle of the generating machine,which latter axis represents the axis of the nominal crown gear. I Thepresent invention may be applied also to the generation of one member ofa gear pair where the other member is non-generated, that is, form-cut.Formula 1 applies to such gear pairs also and it applies, too, to gearpairs in which the two members have unequal dedenda. In the generationof a gear which is to mesh with a mate, non-generated, form-cut gear,usual practice, so far as the generating roll is concerned, may befollowed.

If both members of a gear pair are to be generated with a single-cyclecutter of the described character, then, the cutter axis should be soadjusted relative to the gear blank as if to cut a root angleyr'='yr(ida), where 1 7" denotes the desired root angle.

Broadly the sum of the root angles '71" of both members should besmaller than the sum of the root angles 'y1 by an amount 2(ida) and thedifference of the root angles (yr-yrflmay be split up equally orunequally, as may be desired.

When one gear, usually the larger member of the pair, is produced withthe conventional spread-blade method, that is, two tooth sides are cutsimultaneously, with a standard face-mill angle were gear cutter ofknown type as is preferred in the manufacture of Formate, that is,non-generated, gears, then the generated pinion or smaller member of thepair is out according to the process of the present invention and as ifits root 'yT'='y7 2(id a) H Since each finishing blade of a cutterconstructed according to the present invention is adapted to cut at adefinite point along the length of a tooth, the rotation of the cuttermust be timed to the generating roll. Figures 3 and 4 illustratediagrammatically two different methods of timing the rotation of thecutter to the generating roll. For convenience, it is assumed that theaxis of each cutter is parallel to the axis of the crown gear to whichthe gear being cut is to be generated conjugate, as is the case wherethe gear is generated conjugate to a nominal crown gear.

In Fig. 3, the cutter axis is designated at and the crown gear axis orapex at 9|. 7 A portion of the crown gear-is shown fragmentarily at 92.During the'generating roll, the cutter is rotated on its axis 90, theblank is rotated on its axis which is shown in Fig. 3 projected into theline 93 and simultaneously the axis of the cutter is moved relative tothe work about the apex or axis 9| of the crown gear from position at96' to position 90". The cutter thus rotates in the direction of thearrow 94 and the-work is turned on its axis 93 in direct proportion tothe motion of the cutter about crown gear 'axis 9|. Preferably, also,the generating roll is in direct proportion to therotation 94 of thecutter on its axis'as if a circle 95 circumscribed about the axis 90 ofthe cutter were rolling on a stationary circle 96 concentric with thecrown gear apex 9|.

In the embodiment illustrated in Fig, 4, the cutter rotates on its axisI06 in the direction indicated by the arrow I04 as it is swung about theaxis IOI of the crown gear from the position I03 to the position I00 andthe motion of the cutter is as if a circle I05 circumscribed about theaxis I90 of the cutter were rolling internally on a circle H15concentric to the crown gear apex llll.

Cutters, used in accordancewith the embodiments illustrated in Figs. 3and 4 will cut tooth spaces having the desired taper in depth from endto end when the-heights of the blades of the cutter vary at a uniformrate. In other words, the top cutting edges of a face-mill gear cutterfor practicing the present invention may be arranged to lie in a helixof constant lead whose axis coincides with the axis of the cutter.

Iiet'us now determine the lead of said helix. Referring to Fig. 3, letme denote the ratio of circles 96, 95, that is, the ratio of the cutterrotation to the rotation about crown gear apex 9|.

98 and 99 denote the mean circles'of thecutter blades when the cutteraxis is at the .positions 90' and 90'', respectivelyand llll'denotes themean circle of the blades when the cutter axis is at its mean position9i]. III is a point in the pitch-line element I m at the center of theface of the gear.

Let ds be a very small distance measured along the pitch-line element H0from the point III to a point H3. VH4 is a point on the projected gearaxis 93, which is at the same distance from the crown gear apex 9| asthe point H3,

From Fig. 2 it will be obvious that the further a point in the rootsurface 82 is away from the apex 51, the shallower the cutter should outbecause the further the line 82 is from the line 15. Accordingly, thetool should cut shallower at the point II4 (Fig. 3) than at the point HIby an amount (I I II I4) .tan (i-aa) =ds.cos wtan (ia) We may considerthe motion of the cutter as a bodily motion about apex 9| plus a turningmotion about the cutter center 90. Thebodily motion is through an angleI I3--9I-I I4 to bring the point II3 into position H4. This angle isds.sin g A level of the cutter tip at point I I I, measured axially ofthe cutter by The turning m0- where Lt denotes the sought lead of thetips of the cutter blades. The motion of the cutter about the crown gearaxis or apex SI does not affect the depth of the tooth slots butrotation about the cutter axis 96 does, namely by I ds.sin 11/ 21F A Sowe have the equation sin b ds.cos 1p.tan (t -6a) -ds l+m, and

is also the tangent of the lead angle.

Formula 2 also applies to the showing of Fig. 4 if the ratio me isintroduced as a negative quantity. This will make the resultant leadnegative in the latter case and indicates a lead of opposite hand.

Formula 2 also gives the lead angle of the tip surface of the cutter atthe mean point II I even when the cutter rotation and the rate of rollare not in a constant proportion, as when, for instance, the roll isaccelerated or slowed down near the end of the roll while the cutterrotation remains constant. 7

The shape of the surface in which the tips of the cutter should lie mayalso be determined experimentally by putting a rotating tapered millingcutter embodying the root cone of the gear to be cut inplace of the gearblank, and by milling the proper tip surface on a soft cutter blankwhich is rotated on its axis while being rolled with the said millingcutter as though it were rolling in engagement with the work.

Formula 2 may be a little broadened in scope by putting ('yT- 'yr) inplace of (iaa) so that We have:

where,

, tan (yW-yr). cos 21 T sin t Fig, 5 is a fragmentary axial section of asingle-cycle cutter constructed according to the principles illustratedin Fig. 3. For the purposes of illustration, the cutting portion of thecutter is here represented as though it were a solid body havingopposite side surfaces H5 and H6 and a tip surface II1. Actually,however, the cutting portion of the cutter will be formed by a pluralityof cutting blades, as illustrated in Fig. 12, which extend part-wayaround the peripher of the cutter. These blades are relieved on theirtop and side surfaces to provide tip and side cutting edges.Th'e'surfaces H5, H6 and H1 contain the side and top cutting edges,respectively, of the several blades of the cutter. The blades of thecutter as previously described, are of varying height and the surface II1 which contains the top cutting edges of the blades is a helicalsurface coaxial with the cutter axis I I9.

In th axial section of Fig. 5, the shape of the cutting blade I24 whichis adapted to operate at the large end of the tooth spaces of the gearis shown. Fig. 6 shows the shape of the blade I25 which is adapted tooperate at the center of the tooth face and Fig. '1 shows the shape ofthe blade I26 which is adapted to operate at the small end of the toothspace. It will be noted that all of the blades have straight sidecutting edges and that these side cutting edges lie in conical surfacesI28 and I29, respectively, which are coaxial with the cutter axis II9.It will be noted, further, that the sides of the blades I24, I25 and I26converge in points I30, I3I and I32, respectively, all of which lie in aplane I3 which is perpendicular to the axis II9 of the cutter.

The blades I24, I25 and I26 differ from one another in the amount whichthey occupy of the inverted V formed by their opposite sides. Thus, theblade I25 occupies more of the inverted V than does the blade I24 andlikewise the blade I26 occupies more of the inverted V than does theblade I25. Thus, the length of the active side and of the top cuttingedges of the various blades differ. Hence the blade I26 will cut anarrower slot than the blade I25 when the cutter isadjusted intoengagement with the blank and rotated in engagement therewith. Likewisethe blade I25 will cut a narrower slot than the blade I24.

Blades intermediate the blades I24 and I25 and the blades I25 and I26vary uniformly from one another in height. Thus, the top cutting edgesof the blades lie in the helical surface H1, as shown.

The principles upon which cutters of the present invention operate arefurther illustrated in Figs. 8 to 11 inclusive. In these figures, I10denotes a bevel gear blank to be cut. I1I is the cone apex of this blankand I12 is its axis. One tooth space is shown in the blank. This toothspace is curved longitudinally and inclined to a cone element of theblank.

As previously described, the cutting operation is effected by rotating acutter in engagement with a gear blank while producing a relativerolling movement between the cutter and blank. Fig. 8 illustrates thepoint in the roll at which thecut is taking place at the small end ofthe tooth space of the blank.

I14 is the root circle of the gear at the large end of this tooth spaceand I15 is the root circle of the gear at the small end of the toothspace. I16 is a point at the middle of the small end of I1I, I11 and I18is an axial plane of the gear and passes through the point I16 and theaxis I12 of the gear when the gear is at that position of the roll wherethe small end of the tooth space is being cut. HES-I19 is a root lineelement of the gear lying in this axial plane.

I80 designates a side cutting edge of that blade of the cutter which isadapted to cut at the small end of the gear tooth. I8I is the point ofthis cutting edge which cuts in the root surface of the gear at thesmall end of the tooth space.

The point I8I travels in a plane perpendicular to the axis of the cutteras the cutting edge moves across the face of the blank from one end ofthe tooth to the other in the rotation of the cutter. This plane isdenoted at I82 in Fig. 8. The path of the point I8I of the cutting edgeI80 as it moves across the face of the gear is denoted by the curvedline I83 which lies in the plane I82. The point I84 is the point at thelarge end of the tooth lying in this plane.

The line I03, which denotes the path of the point I8I across the face ofthe blank, will appear as a straight line in Fig. 9, which is a sectionlooking at one side of the tooth space. Here the bottom I85 of the toothspace will appear curved because it is wrapped around the cone of thegear. I

It will be seen, then, from Figs. 8 and 9 that the cutting edge wt ofthe tool which cuts at the small end of the blank will readily clear thelarge end of the blank and not-affect the finishing cut at the largeend.

Between the time that the cutting edge I80 takes its out and the timethat the cutting edge, which is intended to operate at the large end ofthe tooth space of the gear, is ready to take its out, the gear willhave rolled from the position shown in Fig. 8 to that shown in Fig. 10.

I 85 is the point in the middle of the tooth space at the large endthereof. The plane containing the points I1I, I81 and I88 is an axialplane of the blank passing through the point I86 and containing theblank axis I12. The line I86 l8 is the root line of the blank in thisaxial plane. I90 is a side cutting edge of the blade of the cutter whichcuts at the large end of the tooth space and ISl is the point in thisside cutting edge which operates at the bottom of the tooth space at thelarge end of the gear. This point moves in a plane perpendicular to theaxis of the cutter as it passes across the face of the gear blank. Theplane of movement of the point I9I is designated at I92. The point I9Iitself travels in the curved path I93 which lies in the plane I92. I94is a point in this line I93 at the small end of the tooth space. I95 isa point at the bottom of this side of the small end of the tooth space.I95 is a point in the plane I92 and also lying in the axial plane of thework, which plane contains the point I85.

It will be seen that although the point ISI of the cutting edge of theblade which cuts at the large end of the tooth space rotates in a planeI92 which lies below the root surface I15 at the small end of the toothspace by the distance I89I96, interference in depth at the small end ofthe tooth space by the cutting edge I90 is avoided because of thecurvature of the root where the path I93 of the point l9l appears as astraight line and where the bottom I of the tooth space again appearscurved because it is wrapped around'the cone of the blank.

It is because of the change in position of the blank due to the rollbetween operation of different blades of the cutter, then, that bladesof different height can be used to out at different points along thelength of a tooth space, and each blade may cut at a definite pointalong the length of the tooth space.

For cutting gears from the solid, a cutter is employed which has bothroughing and finishing blades. One form of such tool is illustrated inFigs. 12 and 13. The tools shownare intended to operate according to thearrangement shown in Fig. 3. In this method of operation, with thecutter rotating in, the direction of the arrow 94, the cut starts at thesmall end of the tooth space at the beginning of the roll and ends atthe large endof the tooth space at the end of the roll. Accordingly, thecutter will be provided first with a series of roughing teeth I40 to I46inclusive which are of increasing height to cut successively deeper intothe gear blank. These will be followed by a series of finishing teeth,which are designated at I50. The first of these finishing teeth isadapted to finish-cut at the small end of the tooth space, while thelast one is adapted to cut at the large end of the tooth space inaccordance with the principles of the invention already described. Forthis purpose, the finishing teeth also vary in height,

as indicated by the helix I5I which contains the top cutting edges ofthese finishing teeth and which appears as a straight line in thedevelop-- ment of Fig. 13. The first finishing blade I50 cuts at a pointcorresponding to the position of the roll (Fig. 3) and the lastfinishing blade at a point corresponding to the position 90" of theroll. There is a gap I55 between the last finishing blade I50 and thefirst roughing blade I40 and when this gap is abreast of the blank inthe rotation of the cutter, the blank may be indexed and the cutterreturned relative to the blank to its starting position.

The roughing blades l40 to I41 of the cutter preferably will be madewith straight side-cutting edges. They may be made of reduced height andhave their opposite sides, as in the case of the blade I52, convergingat points, such as the point I56, which is situated in the plane I51which also contains the points of convergence of the sides of thefinish-cutting blades. Preferably, however, the roughing blades will bemade so that their opposite side cutting edges form an inverted V ofslightly less dimension than the inverted V of the finishing blades sothat their sides will converge at points which are situated in a planebelow the plane I51. Thus, the inside cutting edges of the finishingblades will be closer to the center of the cutter than the insidecutting edges of the roughing blades and the outside cutting edges ofthe finishing blades will be further away from the center of the cutterthan the outside cutting edges of the roughing blades.

Fig. 15 illustrates a cutter which is adapted to rotate in the oppositedirection from the cutter of Figs. 12 and 13 and which is intended togenerate in the down roll, starting at the large end of the tooth spaceof the gear blank. .The roughing blades I50, as before, are ofsuccessively increasing height, as indicated by the dotted line I62, sothat they cut successively deeper into the blank and the blades IE I,which are the finishing blades, are also. of successively increasingheight. The. tops of these finishing blades are arranged in the helix153, which appears as a straight line in the developed View of Fig. 15.The first finishing blade finish-cuts the large end of a tooth space ofthe blank and the last finishing blade cuts the small end of the toothspace as the cutter rotates in engagement with the blank and rolls withthe blank. There is a gap 165 between the last finishing blade andthefirst roughing blade and the gear blank is indexed when this gap isabreast of the blank and, at the same time the. cutter is returned tostarting position relative to the blank by means of the return roll.

In the case of the cutter shown in Fig. 15, the whole cuttin operationmay be speeded up toward the end of the generating roll because towardthe end of the roll, the cutting is at the small end of the tooth spaceand therefore lightest. Speeding up of the operation includes not onlyacceleration of the generating roll but acceleration of the cutterrotation.

Cutters for operating according to the arrangement illustrated in Fig. 4are similar to the cutters illustrated in Figs. 12 to 15 inclusiveexcept for hand and for this reason no further illustration of thesecutters need be required.

In the embodiments of the invention already described, the cutter isintended to operate during relative roll of the cutter and blank in onedirection. Fig. 16 illustrates diagrammatically a modified form ofcutter which is adapted to operate during roll in both directions. Onlya few of the blades of the cutter are shown in the fragmentary viewgiven. This cutter is intended to rough-cut during roll in one directionand finish-cut during the return roll. As a result, the blades arearranged so that their tips lie in helices which are inclined inopposite directions with reference to the axis 2|5 of the cutter. Theblades 20% to 295 inclusive are roughing blades and the blades 206 to2!! inclusive are finishing blades. The blades 205 and 206 are adaptedto rough-cut and finish-cut, respectively, at the small end of the toothspaces during roll in opposite directions, while the blades 233i) and 2are adapted to operate further along the tooth space toward the heel orlarge end of the tooth space. The top cutting edges of the roughingblades lie in a helix 2 l 6 and the top cutting edges of the finishingblades lie in a helix H1. The helices appear as straight lines indevelopment.

Preferably, the roughing blades 260 to 205 are made to be of slightlysmaller point width than the finishing blades which means that theopposite side cutting edges of the roughing blades will converge inpoints which lie in a plane 2i8 that is perpendicular to the axis 2I5 ofthe cut ter but which is below the plane 219 in which the points ofconvergence of the sides of the finish-cutting blades 206 to 2| I lie.

Another embodiment of the invention is illustrated in Fig. 1'7. Here thepoints of convergence of the side-cutting edges of the finishing bladesdo not lie in a plane but in a helical surface 225. Such helicalarrangement of the inverted V shape of the side-cutting profiles enablesus to control bias bearing, as will now be described.

In my United States Patent No. 1,930,365, a method has been disclosedfor cutting simultaneously two sides of gear teeth without bias bearing.This method enables us to cut two sides of the teeth of a spiral bevelor hypoid gear simultaneously while nevertheless obtaining a squaretooth bearing on both sides. Bias control is also useful to counteractdistortion of the teeth of the gear during hardening and it permits ofprecorrecting the gears for hardening changes.

The method described in my prior patent mentioned consists in adding astraight line motion to the relative rolling motion between the cutterand the work, the straight line motion being preferably in the directionof the axis of the basic gear to which the gear being cut is generatedconjugate or in the direction of the cutter axis.

To eliminate the requirement for this additional motion and still obtainbias control, a cutter such as illustrated in Fig. 1'7 may be used forwhen such a cutter is turned on its axis, it

' is the equivalent of a face-mill which is turned on its axis and whichsimultaneously moves along said axis. Certain slight difierences in theaction will be explained fully hereafter. With the helical type ofcutter illustrated in Fig. 17, then, we may. obtain simultaneous biascontrol on both sides of the teeth of the gear without any added motion,the motion along the cutter axis being unnecessary. The operation of a.helical cutter in the cutting of a gear blank according to the presentinvention will now be described. In Fig. 18,, 230- denotes the apex of abevel pinion or gear Whose axis is projected into the line 23l and whosedeveloped pitch surface is shown at 232. In the method of my priorpatent, the gear or pinion being cut may be generated conjugate eitherto a basic gear whose axis intersects the axis of the blank or whoseaxis is offset from the axis of the blank. The same is true in thecutting of gears with a helicalcutter according to the presentinvention. For the purposes of illustration, it is assumed that the gear232 in Fig. 18 is to be'generated conjugate to a basic gear whose axis233 is offset from the axis of the blank. For convenience, also, it isassumed that the axis 234 of the cutter is parallel to the axis 233; ofthe basic gear.

235 denotes an exaggerated section through the cutting blades of acutter of the general type but of the opposite hand of helix from thatshown in Fig. 17, the section being taken in a plane perpendicular tothe cutter axis. For convenience of illustration, the cutter is shown asthough its cutting portion were solid and did not consist of individualcutting blades. 240 denotes the outside cutting surface and 242 theinside cutting surface of the cutter, that is, the lines which containthe outside and inside cutting edges of the cutter in the plane shown.

The cutter is assumed to be rotating in the direction of the arrow 236during the up-roll and the timing of the cutter to the roll is as thoughthe circle 23'! circumscribed about the axis of the cutter were rollingon the circle 238 concentric with the axis 233 of the basic generatinggear. With the direction of rotation of the cutter indicated, the highpoint in the helical surface 225 (Fig. 17) of the cutter will enter thetooth space of the blank first. In the plane of Fig. 18, then, thecutting portion of the cutter will appear as a section 235 which isthinned down from left to right. The cutter has in a sense, then, acircular cutting portion which is moved back along the axis of thecutter during the up-roll. In Fig. 18, the pinion is assumed to be abovethe drawing plane and consequently to be left-handed.

The outside cutting surface 240 of the helicoidal cutter can beconsidered as an involute helicoid whose curvature equivalent is knowntobe a conical surface having an axis 24! parallel to the cutter axis andlocated on the base circle of the helicoid. Likewise, the inside surface242 of the cutter can be represented by a conical surface whose axis isat 243. The distance of the axis 24] from the axis 234, or of the axis243 from the axis 234, is equal to the base radius of the involutehelicoid in question. It is equal to where c is the pressure angle ofthe cutter surface in a normal plane tangent to the base cylinder andwhere L denotes the cutter lead or advance per complete turn.

The analogy with the method of my prior patent is now complete. Ahelical cutter constructed according to the present invention producesprecisely the same results on the tooth sides of a gear blank as twocutters of the facemill type whose centers 24! and 2 83 are closetogether.

If this helical cutter "had a constant point width, it would produce adedendum angle on the blank which is slightly smaller than the dedendumangle produced by a face-mill which is moved along its axis during theroll according to the method of my prior patent. The decrease indedendum angle is determined by the inclination :i of the projectedtangent 245 to the helix235.

rtan (to determined as if the root angle of the pinion or 5 gear were('y7"fl'). To produce the desired root angle, 71 the point width of thetool is changed around the cutter circumference as described before andit is believed unnecessary to repeat here the computation forestablishing the rate of change of the cutting point width. The cutterpoint width can also be determined experimentally as pointed out above.7

Fig. 19 illustrates the relations which exist between the cutter and thegear blank when the cutter rotation is so timed with the roll as thoughthe circle 24! circumscribed about the axis 244 of the cutter wererolling internally on a stationary circle 248 concentric with the axis253 of the basic gear to which the gear 252 being cut is to be generatedconjugate. The helix in which the points of convergenceof the oppositeside cutting edges of the cutter lie is denoted at 255. 256 and 25'!denote, respectively, the helices in which the outermost points of theoutside and inside cutting edges of the different blades of the cutterlie.

In the case illustrated in Fig. 19, the lead of I the helical cutterthread should be left hand to is'of left hand, whereas a right handcutter thread was used in the embodiment illustrated in Fig. 18 toproduce a left hand pinion. The width of a section through the cutterthread 255 taken in a plane perpendicular to the axis 244 of the cutter,then,- is reduced from right to left at the zone of cutting engagement.A line 259 tangent to the helix 255 is then inclined oppositely to aplane perpendicular to the axis of a 10 cutter as compared with thedirection of inclination of the tangent 245 in Fig. 18. The angle 7should, therefore, be used as a negative quantity in determining theimaginary root angle r'y' of the pinion. The negative value of a mayalso be obtained from the formula for tangent 7 when the lead L of thecutter thread is introduced as a negative quantity.

Fig. 20 is a fragmentary sectional view of a cutter intended toillustrate the fact that various cutters having the same inverted Vcontour or profile may be substituted for one another in order tocontrol the lengthwise bearing or contact of the teeth of mating gearsas is common practice for ordinary face-mill cutters. So, in place of acutter whose axis is at 25I and one whose blade is denoted in dottedlines at 262 a cutter may be used whose axis is at 263 and one of whoseblades is shown in section at 264. The blade 26 1 has sides whichconverge in a point 265 which is also the point of convergence of theopposite sides of the blade 262 of the cutter 260. It is readilyunderstood in the art that by substituting one of these cutters for theother, the tooth bearingmay be more localized lengthwise of the gearteeth inasmuch as the mean normal cutter radius 266251 has beenincreased to 266- 468 0n the outside cutting surface of the cutter andinasmuch as the mean outside normal cutter radius 210-2 of the insidecutting surface of the cutter has been decreased to Figs. 21 and 22 showa cutter which is intended, like the cutter illustrated in Fig. 18, toturn in the counter-clockwise direction denoted by the arrow 236 duringthe up-roll. Only a few of the blades are shown. This cutter has aplurality of roughing blades of gradually increasing height whichprecede the finishing blades. Both the roughing and finishing bladeshave opposite side surfaces remove bias on a spiral bevel pinion or gearwhich 25 tooth space.

0 of the same pressure angle.

The opposite side cutting edges of the roughing blades converge inpoints which lie in the same helix 285 as do the points of convergenceof the opposite side-cutting edges of the finishing blades or broadly ina helix of the same lead. Thus, as shown in Fig. 22, the opposite sidecutting edges 283 and 284 of the roughing blade 213 converge in a point214 lying on the helix 285 while the opposite side cutting edges of thefinishing blades 275, 216 and 211 converge in points 280, 2i3l and 282,respectively, which lie on this same helix 285. The roughing blades areof gradually increasing height and successive roughing blades simplyoccupy varying amounts of the inverted V formed by their opposite sides.Thus, as indicated in Fig. 21, the actual top cutting edges of theroughing blades lie in a helical surface 235. With the arrangementdescribed, the roughing blades are of gradually increasing heightleading up to the first finishing blade 215.

The first finishing blade 215 is for finish-cutting the tooth space atthe small end thereof.

The succeeding finishing blades are each adapted to cut at differentpoints along the length of the They have gradually increasingpoint-width and their tips are at gradually increasing distances fromthe helix 285. In other words, their tip cutting edges lie in a helix281 which is inclined to the helix 285. The final finishing blade isadapted to finish-cut at the large end of the tooth space and isfollowed by a gap 288. When this gap is abreast of the blank, the cuttercan be returned relative to the blank to starting position and the blankmay be indexed.

Figs. 23 and 24 illustrate a cutter such as may be employed where thecutter rotates in a clockwise direction during the up-roll as indicatedby the arrow 2A6 in Fig. 19. This cutter also has a plurality ofroughing blades which are of increasing height and whose tip cuttingedges lie in a helix 298. The points of convergence of the oppositeside-cutting edges of the rough-cutting blades may lie in the same helix292 in which the points of convergence of the opposite side cuttingedges of the finishing blades lie. The roughing blades precede afinishing blade 293 which is adapted to cut at the small end of thetooth space. The succeeding finishing blades such as the blades 294 and295 of this cutter are adapted to cut at different points further alongthe tooth space toward the large end of the tooth. The finishing bladesare of gradually decreasing height and point width and their tip-cuttingedges lie in a helix 296 which is angularly disposed to the helix 292.There is a gap 281, as before, between the last finishing blade and thefirst roughing blade to permit of the indexing and return roll.

Figs. 25 and 26 show a cutter which is adapted to rotate in acounter-clockwise direction and cut during the down roll. In this case,the first finish-cutting blade 300 is for finish-cutting the large endof the tooth spaces of the blank and the last finish-cutting blade isfor cutting the small end of the tooth space. Intermediate cuttingblades, such as the blades 39! and 302, out at difierent points alongthe tooth space between the large and the small ends thereof. The pointsof convergence of the opposite side cutting edges of the finishingblades lie in a helix 305 whereas these blades increase in height anddecrease in point width and have their tip cutting edges lying in ahelix 361 which is inclined to the helix 305.

This cutter is provided with a plurality of roughing blades which are ofincreasing height and precede the first finishing blade 300. The

.tip cutting edges of these blades are arranged in Lm m where me is thenumber of revolutions of the cutter in a revolution of the cutter center234 (Fig. 18) about the basic gear axis 233. Of

course, in actual practice, the cutter center only moves through a partof a revolution about the basic gear axis 233 in the generation of atooth space of a gear.

In determining Lm, the angle (2i+7'g+7'P) is used in place of the sum ofthe dedendum angles. 2' is given in Formula 1 and jg and 91 are theangles ;i for gear generation and pinion generation, respectively.

A suitable match of the profiles of the mating gears or profile mismatchmay be obtained by varying the pitch angle of the basic gear to whichthe pinion is formed conjugate and which is represented by the tool. Areduced pitch angle of the basic gear gives increased profile mismatch,as will readily be understood.

The lead L as determined above is for the case where a helical cutter isused on the pinion only. If both members of the pair are cut with ahelical cutter, the lead L may be split up equally or unequally, as maybe desired. When a full profile match is desired, the lead Lm'forobtaining a square tooth bearing is:

7P is zero when no lead is provided on the inverted V shape of thecutter profile, that is, when the points of convergence of the oppositesides of the finishing blades of the cutter all lie on a circle, thatis, in a plane perpendicular to the axis of the cutter. 7' may bepositive, as in the example shown in Fig. 18 or negative as in Fig. 19.

The above described method which uses a helical cutter in the generationof at least one member of the pair is very practical as it permitscutting both sides of a tooth space simultaneously to the desired rootangle without additional generating motion, while allowing full controlof the tooth bearing, namely, of the length and width of tooth bearing.Bias bearing may be eliminated entirely or reduced to any desiredextent.

Ihe process employing a helical cutter is also applicable to thegeneration of hypoid gears conjugate to a basic helicoidal segment suchas described in my Patent No. 1,676,371 of July 10,

1928. The helical cutter may represent such a basic helicoidal segmentfor the helical arrangement of the points of convergence of the oppositesides of the cutting blades permits of eliminating an axial motion andthe cutter may be used to represent a helicoidal segment by simplyrotating the cutter on its axis while producing a rolling motion betweenthe cutter and blank about an axis representing the axis of thishelicoidal segment.

Figs. 27 to 32 inclusive illustrate how the method of the presentinvention may be applied to the cutting of a spiral bevel or hypoidpinion conjugate to a gear whose tooth surfaces have been out two sidessimultaneously by cutting the pinion with a female tool which iscomplementary to the male tool employed in the manufacture of the gear.

In Fig. 27, 3|5 denotes the pinion to be cut. Its axis is designated at3l6 and its apex at 3.

The axis of the mate gear is designated at 3| 8.

This mate gear is here assumed generated in the conventional mannerconjugate to a nominal crown gear having an axis 3l9 perpendicular tothe root plane of the gear.

It is well known that fully matched tooth surfaces may be obtained onthe gear and pinion when the pinion is cut with a female tool which isexactly complementary to the male tool which is employed to cut the gearand whose axis coincides with the axis of the gear cutter. In otherwords, the pinion 3| 5 might be cut to fully match the tooth surfaces ofits mate gear by using a female cutter 320 which straddles and isexactly complementary to the male cutter 32l employed in the cutting ofthe gear. The pinion cutter 320 will then represent a tooth space of thenominal crown gear to which the gear was generated conjugate. It hastwoconcentric rows of cutting blades and these are adapted tocut'opposite sides of a tooth of the pinion simultaneously. Generationof the pinion is effected by producing a relative rolling movementbetween the cutter and the pinion blank as if the crown gear and pinionwere meshing together.

The obvious draw-back of such generation hitherto has been the factthatit has been necessary to cut the tooth spaces of uniform depth fromend to end and consequently the teeth have been weak at their small endsand undercut on the pinion. If the female cutter is made, however, inaccordance with the present invention so that each finish-cutting edgeof the cutter is adapted to cut at some definite point along the lengthof the teeth and the rotation of the cutter is timed with the generatingroll, a pinion can be generated whose teeth taper in depth from end toend. The desired taper in depth can be obtained by simply adapting theheight of the cutting edges of the female tool to the tooth depthdesired at the point where each cutting edge cuts.

The required constructionof the female tool is indicateddiagrammatically in Fig. 31. 325 denotes the sides of a tooth space ofthe crown gear or the opposite side cutting edges of the cutter whichcuts the gear. 326, 326; 321, 321; and 328, 328 denote different cuttingblades of the female cutter which is complementary to the gear cutterand which is adapted to represent thesides 325 of a tooth space of thecrown gear teeth and cut opposite sides of the teeth of the pinion. Theblades 326, 326'; 321, 321' and 328, 328' are arranged in pairs whichare adapted to cut opposite sides of a tooth of the pinion 'in .arevolution of the cutter. The different pairs of blades are of varyingheight around the cutter. In the embodiment shown, the adjacent sidecutting edges of the different pairs of blades converge in points 329which lie all in the same plane perpendicular to the axis of the cutter.The cutter might be made, however, so that the points of convergencewould lie in a helix for the purpose above described.

The cutting blades 3%, 325 are adapted to cut at the small end of atooth of the pinion. The cutting blades 321, 321' have a height to cutat the center of a tooth of the pinion and the cutting blades 328, 328'have a height adapted to properly form the large end of the tooth. In asingle cycle female cutter, there will be provided, of course, severalcutting blades intermediate the blades which cut at the small end andthose which cut at the center and intermediate those which cut at thecenter and those which cut at the large end, the number depending. ofcourse, upon the smoothness of finish desired upon the pinion tooth out.

In Fig. 28, the female cutter is shown diagrammatically and at a meanposition of the roll.

so that the axis of the cutter describes the are 332. When the gap inthe cutter is abreast of the blank, the blank is indexed and the cutteris returned relative to the blank to starting position.

Figs. 29 and 30 illustrate how the method of cutting with a femalesingle cycle cutter constructed according to the present invention maybe applied to the generation of a pinion conjugate to a non-generated orFormate gear. 335 is the pinion to be cut and 34! denotes its mate,non-generated gear. 336 designates the axis of the pinion and 342 theaxis of the gear.

These axes are shown at right angles to one another. The femalesingle-cycle cutter 340 used for cutting the pinion has an axis 344which coincides with the axis of the gear cutter and occupies the sameposition with respect tothe axis of the cradle of the pinion cuttingmachine as the gear cutter does with respect to the gear axis. Thefemale cutter represents a tooth space of the mate gear 3. The femalecutter, as in the previously described embodiment of the 'invention, hascutting blades of varying height around its periphery which are adapted,respectively, to cut at definite points along the length of a tooth andthereby cut the teeth on the pinion of proper taper in height from endto end. The teeth of the pinion are generated by rotating the cutter 348on its axis 344 and simultaneously effecting a relative rolling movementbetween the cutter and the pinion blank as though the pinion blank wererolling with its mate gear 3M. When the gap in the cutter is abreast ofthe blank, the blank is indexed and the cutter is returned relative tothe blank to starting position. Fig. 30 shows a mean position in thegenerating roll.

For cutting pinions from the solid, a female cutter may be used such asshown in Figs. 33 and 34. This cutter has its blades arranged, asbefore, in two concentric rows 33'! and 338 part- 1 way around itsperiphery and there is an index this invention so that differentfinishing blades will finish-cut at dilferent definite points alongthelength of a tooth during the generating roll and in a revolution ofthe cutter.

The variation in height of the roughing blades is indicateddiagrammatically in Fig. 33 by the lines 345' and 345 and the variationin height of the finishing blades by the lines 34'! and 3 23'. Theselines represent the helices in which the top cutting edges of therespective blades lie. The opposite side cutting edges of the finishingblades converge preferably in points lying on a circle in a planeperpendicular to the axis 353 of the cutter or they may converge inpoints lying on a helix coaxial withthe cutter according to thepreviously described principles of the invention. The opposite sidecutting edges of the roughing blades may converge in the same circle orin the same helix on which the points of convergence of the finishingblades lie or may converge on different circles or a difierenthelix,-also according to previously described principles of theinvention.

It will be noted that, as indicated in Fig. 33, the blades in the outerrow 33'! are slightly

